TE2021

Problema 3

# Problema3.2

Para cada uno de los 10 dígitos (0,…,9) se tienen 200 imágenes digitalizadas del dígito escrito a mano. De cada imagen se obtuvieron 649 características (“features”). Se trata de predecir el digito correspondiente a una imagen, en función de sus características. Los datos están repartidos en 6 archivos, todos con m=2000, cada uno de los cuales corresponde a un tipo de características: mfeat-fou, -fac, -kar, -px-, zer-. mor. De modo que luego hay que “pegarlos”. Las primeras 200 filas de cada archivo corresponden a la clase “0”, las siguientes 200 a “1”. etc. Aplique los métodos que le parezcan convenientes y compare sus performances. Los datos están en http://archive.ics.uci.edu/ml/datasets/Multiple+Features

1. mfeat-fou: 76 Fourier coefficients of the character shapes;
2. mfeat-fac: 216 profile correlations;
3. mfeat-kar: 64 Karhunen-Love coefficients;
4. mfeat-pix: 240 pixel averages in 2 x 3 windows;
5. mfeat-zer: 47 Zernike moments;
6. mfeat-mor: 6 morphological features.

---

DATOS

fou<-read.table("mfeat-fou",header=FALSE)
fac<-read.table("mfeat-fac",header=FALSE)
kar<-read.table("mfeat-kar",header=FALSE)
pix<-read.table("mfeat-pix",header=FALSE)
zer<-read.table("mfeat-zer",header=FALSE)
mor<-read.table("mfeat-mor",header=FALSE)

#mor$V1<-as.factor(mor$V1)
#mor$V2<-as.factor(mor$V2)
#mor$V3<-as.factor(mor$V3)


mfeat<-cbind(fou,kar,pix,zer,mor,fac)
colnames(mfeat)<-as.vector(seq(1,649,1))#as.vector(seq(1,649,1))
class<-rep(0,2000)
class[(1:200)]<-0
class[(201:400)]<-1
class[(401:600)]<-2
class[(601:800)]<-3
class[(801:1000)]<-4
class[(1001:1200)]<-5
class[(1201:1400)]<-6
class[(1401:1600)]<-7
class[(1601:1800)]<-8
class[(1801:2000)]<-9
class<-as.factor(class)
datos<-cbind(mfeat,class)

## DESCRIPTIVO DE LOS DATOS

str(mor)

TRAIN-TEST

set.seed(100)
n = nrow(datos)
trainIndex = sample(1:n, size = round(0.7*n), replace=FALSE)
ds.train = datos[trainIndex ,]
ds.test = datos[-trainIndex ,]
ds.train.x = subset(ds.train, select=c(-class))
ds.test.x = subset(ds.test, select=c(-class))

table(ds.train$class)

  0   1   2   3   4   5   6   7   8   9 
129 147 144 136 146 143 148 134 132 141 

table(ds.test$class)

 0  1  2  3  4  5  6  7  8  9 
71 53 56 64 54 57 52 66 68 59 

——————————————————————————–

---

LDA

library(MVN)

Outliers y Contraste de Normalidad

XX<-model.matrix(lm(class~.,data=ds.train))
Xtest<-model.matrix(lm(class~.,data=ds.test))

outliers <- mvn(data = fou, mvnTest = "hz", multivariateOutlierMethod = "quan")

No esto estoy pudiendo computar los outliers con todas las variables. No está claro si tiene sentido mirarlo así.

Lo mismo con los test de contraste por nomalidad multivariado, rompen cuando sumo variables. Pareciera queno puede calcular la inversa.

royston_test <- mvn(data = mfeat, mvnTest = "royston", multivariatePlot = "qq")

royston_test$multivariateNormality

hz_test <- mvn(data = subset(ds.train, select=c(1:132,135:230,231:242,245:260,500:600)), mvnTest = "hz")
hz_test$multivariateNormality

Veamos la normalidad por variable. Ya es obvio que no va a ser normalmultivariado. Si no es normal por variable, no puede ser normal multivairado. 

# Contraste de normalidad Shapiro-Wilk para cada variable en cada especie
library(reshape2)
library(knitr)
library(dplyr)

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union

datos_tidy <- melt( subset(ds.train,select=c(-292,-369,-370,-200,-183,-261,-276,-306,-291,-305,-290,-275,-268,-430,-428,-253,-399,-416,-469,-477,-492,-484,-491,-502,-506,-521,-522,-585,-586,-507,-508) ), value.name = "valor")

Using class as id variables

                           
#select=c(-369,-370,-200,-183,-261,-276,-306,-291,-305,-290,-275,-268,-430,-428,-253,-399,-416,-469,-477,-492,-484,-491,-502,-506,-521,-522,-585,-586,-507,-508) ), value.name = "valor")
kable(datos_tidy %>% group_by(class, variable) %>% summarise(p_value_Shapiro.test = shapiro.test(valor)$p.value))

`summarise()` has grouped output by 'class'. You can override using the `.groups` argument.

class	variable	p_value_Shapiro.test
0	1	0.0000033
0	2	0.0038901
0	3	0.0000316
0	4	0.0032850
0	5	0.2716876
0	6	0.0000000
0	7	0.0126372
0	8	0.0000438
0	9	0.0003343
0	10	0.0511716
0	11	0.0000006
0	12	0.1356695
0	13	0.0004005
0	14	0.0303504
0	15	0.0001554
0	16	0.0000004
0	17	0.0002864
0	18	0.0000006
0	19	0.0000002
0	20	0.0350572
0	21	0.0000068
0	22	0.0010951
0	23	0.0001113
0	24	0.0000744
0	25	0.0051919
0	26	0.0072637
0	27	0.0225675
0	28	0.0000236
0	29	0.0000589
0	30	0.0418708
0	31	0.0000695
0	32	0.0022156
0	33	0.0020379
0	34	0.3260611
0	35	0.0355078
0	36	0.0165869
0	37	0.1826677
0	38	0.0016429
0	39	0.0012273
0	40	0.0330816
0	41	0.0057053
0	42	0.2666183
0	43	0.0037215
0	44	0.2956729
0	45	0.0099593
0	46	0.0721195
0	47	0.0060155
0	48	0.0032297
0	49	0.0000341
0	50	0.0211419
0	51	0.0025536
0	52	0.0024766
0	53	0.0001696
0	54	0.0165374
0	55	0.0000009
0	56	0.0539523
0	57	0.0000149
0	58	0.2007079
0	59	0.0044383
0	60	0.0029107
0	61	0.0000965
0	62	0.0417331
0	63	0.0009794
0	64	0.0000349
0	65	0.0000012
0	66	0.0000020
0	67	0.0000006
0	68	0.0000000
0	69	0.0000001
0	70	0.1569376
0	71	0.0000010
0	72	0.0017773
0	73	0.0000000
0	74	0.3648599
0	75	0.0002566
0	76	0.0000006
0	77	0.0000023
0	78	0.0099600
0	79	0.2265510
0	80	0.0003089
0	81	0.0002769
0	82	0.0156941
0	83	0.0004866
0	84	0.4894592
0	85	0.0966993
0	86	0.8683843
0	87	0.0141213
0	88	0.0007608
0	89	0.0000329
0	90	0.8428408
0	91	0.6457921
0	92	0.0574667
0	93	0.0797003
0	94	0.0126780
0	95	0.2093022
0	96	0.8354477
0	97	0.3314201
0	98	0.3260628
0	99	0.3993888
0	100	0.4415538
0	101	0.8974428
0	102	0.9062373
0	103	0.0061198
0	104	0.3562879
0	105	0.6675252
0	106	0.5005090
0	107	0.7199764
0	108	0.6986178
0	109	0.7742485
0	110	0.4793113
0	111	0.9473561
0	112	0.7237047
0	113	0.2756036
0	114	0.7691244
0	115	0.1527751
0	116	0.4886371
0	117	0.9232960
0	118	0.3612713
0	119	0.4199597
0	120	0.2765711
0	121	0.0015768
0	122	0.4752904
0	123	0.7335492
0	124	0.1873832
0	125	0.5872727
0	126	0.1334630
0	127	0.0059653
0	128	0.1219874
0	129	0.9300515
0	130	0.5749788
0	131	0.3696554
0	132	0.2813940
0	133	0.6975466
0	134	0.8716048
0	135	0.6922543
0	136	0.3972503
0	137	0.2529261
0	138	0.1723081
0	139	0.2281410
0	140	0.8923086
0	141	0.0000000
0	142	0.0000000
0	143	0.0000000
0	144	0.0000000
0	145	0.0000000
0	146	0.0000000
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0	148	0.0000000
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0	161	0.0000000
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0	165	0.0000000
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0	167	0.0000000
0	168	0.0000000
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0	170	0.0000000
0	171	0.0000000
0	172	0.0000000
0	173	0.0000000
0	174	0.0000000
0	175	0.0000000
0	176	0.0000000
0	177	0.0000000
0	178	0.0000000
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0	180	0.0000000
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0	184	0.0000000
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0	186	0.0000000
0	187	0.0000000
0	188	0.0000000
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0	190	0.0000000
0	191	0.0000000
0	192	0.0000000
0	193	0.0000000
0	194	0.0000000
0	195	0.0000000
0	196	0.0000000
0	197	0.0000000
0	198	0.0000000
0	199	0.0000000
0	201	0.0000000
0	202	0.0000000
0	203	0.0000000
0	204	0.0000000
0	205	0.0000000
0	206	0.0000000
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0	383	0.0001142
0	384	0.0001067
0	385	0.0141917
0	386	0.0000693
0	387	0.9192936
0	388	0.0000000
0	389	0.0000201
0	390	0.0000040
0	391	0.0001024
0	392	0.0003086
0	393	0.0000042
0	394	0.0000000
0	395	0.0000034
0	396	0.0000001
0	397	0.0000000
0	398	0.1800313
0	400	0.0000174
0	401	0.0000005
0	402	0.0008352
0	403	0.0003664
0	404	0.0003033
0	405	0.0000002
0	406	0.0000000
0	407	0.0000000
0	408	0.0258717
0	409	0.0002107
0	410	0.0000002
0	411	0.0008008
0	412	0.0000080
0	413	0.0002918
0	414	0.0000000
0	415	0.0000001
0	417	0.0000988
0	418	0.0003944
0	419	0.0000012
0	420	0.0000000
0	421	0.0000001
0	422	0.8690279
0	423	0.3259627
0	424	0.0000001
0	425	0.0000061
0	426	0.3249642
0	427	0.0755049
0	429	0.0000000
0	431	0.0000000
0	432	0.0000000
0	433	0.0000000
0	434	0.0000082
0	435	0.0000021
0	436	0.0001244
0	437	0.0338244
0	438	0.6039664
0	439	0.0110563
0	440	0.0000000
0	441	0.0000000
0	442	0.0000000
0	443	0.0000003
0	444	0.0000059
0	445	0.0000017
0	446	0.7925875
0	447	0.1780826
0	448	0.0828751
0	449	0.9278102
0	450	0.6848066
0	451	0.0000000
0	452	0.0000025
0	453	0.0000277
0	454	0.0009412
0	455	0.0000390
0	456	0.0000182
0	457	0.0000552
0	458	0.6118722
0	459	0.0254665
0	460	0.0851664
0	461	0.0644805
0	462	0.0009014
0	463	0.0000009
0	464	0.0000001
0	465	0.0000004
0	466	0.0190248
0	467	0.0000940
0	468	0.0000351
0	470	0.3599476
0	471	0.0040246
0	472	0.0000012
0	473	0.0192582
0	474	0.0017651
0	475	0.0000537
0	476	0.0000108
0	478	0.0001050
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0	480	0.0020892
0	481	0.0000799
0	482	0.1180652
0	483	0.0000031
0	485	0.0005191
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0	488	0.0000000
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0	493	0.0563417
0	494	0.0628125
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0	497	0.0245228
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0	499	0.0000000
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0	503	0.0000004
0	504	0.0000006
0	505	0.0000423
0	509	0.0007542
0	510	0.0023351
0	511	0.0000000
0	512	0.0001086
0	513	0.0000458
0	514	0.0008625
0	515	0.0005504
0	516	0.0000014
0	517	0.0032916
0	518	0.0999533
0	519	0.0045553
0	520	0.0129721
0	523	0.0000000
0	524	0.0000111
0	525	0.0000071
0	526	0.0037460
0	527	0.0000000
0	528	0.0017177
0	529	0.0514649
0	530	0.4968493
0	531	0.8020109
0	532	0.0027327
0	533	0.0117863
0	534	0.1257451
0	535	0.0000000
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0	538	0.0029338
0	539	0.0010658
0	540	0.0002428
0	541	0.0365524
0	542	0.0326311
0	543	0.1182264
0	544	0.0011748
0	545	0.0100991
0	546	0.0011114
0	547	0.9660134
0	548	0.0000013
0	549	0.0000000
0	550	0.0385361
0	551	0.0000701
0	552	0.0000417
0	553	0.0000363
0	554	0.0902897
0	555	0.0233636
0	556	0.0014009
0	557	0.0054072
0	558	0.0001433
0	559	0.0000000
0	560	0.0000152
0	561	0.0000000
0	562	0.0000004
0	563	0.0173567
0	564	0.0002885
0	565	0.0000042
0	566	0.0434076
0	567	0.3988704
0	568	0.0013114
0	569	0.0019628
0	570	0.0257767
0	571	0.0000000
0	572	0.0000000
0	573	0.0000000
0	574	0.0000001
0	575	0.0156582
0	576	0.0000554
0	577	0.0000333
0	578	0.0016029
0	579	0.0059936
0	580	0.0015758
0	581	0.0133705
0	582	0.0005911
0	583	0.0000000
0	584	0.0000000
0	587	0.0001142
0	588	0.0004721
0	589	0.1392938
0	590	0.5492964
0	591	0.0000000
0	592	0.0622354
0	593	0.0000681
0	594	0.0024730
0	595	0.0000000
0	596	0.0000152
0	597	0.0000214
0	598	0.0017771
0	599	0.0001207
0	600	0.0000351
0	601	0.1202351
0	602	0.6114125
0	603	0.0000000
0	604	0.0000027
0	605	0.5381455
0	606	0.0000070
0	607	0.0000000
0	608	0.0000017
0	609	0.0000080
0	610	0.0070261
0	611	0.0659843
0	612	0.0000037
0	613	0.0029956
0	614	0.5788463
0	615	0.6349322
0	616	0.0003053
0	617	0.5033265
0	618	0.0000529
0	619	0.2283166
0	620	0.0000152
0	621	0.0000000
0	622	0.0005659
0	623	0.0000001
0	624	0.0104583
0	625	0.0008356
0	626	0.1991301
0	627	0.0798294
0	628	0.2273642
0	629	0.0674148
0	630	0.3698568
0	631	0.0000000
0	632	0.0000001
0	633	0.0000000
0	634	0.0158777
0	635	0.0012680
0	636	0.0066238
0	637	0.0000014
0	638	0.5255186
0	639	0.0003016
0	640	0.0000221
0	641	0.0000128
0	642	0.0036366
0	643	0.0029274
0	644	0.0000004
0	645	0.0000000
0	646	0.0003552
0	647	0.0000276
0	648	0.0000127
0	649	0.0102149
1	1	0.0184408
1	2	0.0000609
1	3	0.0056310
1	4	0.0078996
1	5	0.0000864
1	6	0.0000038
1	7	0.0156125
1	8	0.0046354
1	9	0.4706963
1	10	0.0097401
1	11	0.0406401
1	12	0.2846142
1	13	0.0316629
1	14	0.0195787
1	15	0.0000577
1	16	0.5962550
1	17	0.2589723
1	18	0.1170849
1	19	0.0019052
1	20	0.7162318
1	21	0.3631634
1	22	0.8093311
1	23	0.0000570
1	24	0.0059408
1	25	0.7251159
1	26	0.0158766
1	27	0.2068631
1	28	0.0237811
1	29	0.0063856
1	30	0.0295706
1	31	0.9141458
1	32	0.7651569
1	33	0.0395074
1	34	0.0052713
1	35	0.3367241
1	36	0.2105351
1	37	0.2776905
1	38	0.1117622
1	39	0.2608134
1	40	0.3496978
1	41	0.1033971
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ds.shapiro = datos_tidy %>% group_by(class, variable) %>% summarise(p_value_Shapiro.test = shapiro.test(valor)$p.value)

`summarise()` has grouped output by 'class'. You can override using the `.groups` argument.

ds.shapiro

p1 <- ggplot(data = ds.shapiro, aes(x = p_value_Shapiro.test , fill = class)) +
      geom_histogram(position = "identity", alpha = 0.5, bins = 50)+
      geom_vline(xintercept = 0.05, linetype ='dashed', color = 'blue', size = 2) +
      scale_x_continuous("p-valor Shapiro-Test") 

png(filename = "Shapiro-Test.png", width = 800, height = 600)
show(p1)
dev.off()

null device 
          1 

ggarrange(p1, nrow = 1, common.legend = TRUE)

 ggplot(data = subset(datos_tidy, variable==33), aes(x = valor, fill = class)) +
      geom_histogram(position = "identity", alpha = 0.5, bins = 20)

# Representación de cuantiles normales de cada variable para cada especie 
for (i in 0:9) {
    x <- subset(datos_tidy, variable==357 & class == i)$valor
    qqnorm(x, main = paste("class", i), pch = 19, col = i + 1)
    qqline(x)
  }

covarianza

# devtools::install_github("arsilva87/biotools")
library(biotools)

---
biotools version 4.2

boxM(data = mfeat, grouping =datos$class)

there are one or more levels with less observations than variables!

    Box's M-test for Homogeneity of Covariance Matrices

data:  mfeat
Chi-Sq (approx.) = Inf, df = 845649, p-value < 2.2e-16

——————————————————————————–

---

Discriminante

library(MASS)

Attaching package: ‘MASS’

The following object is masked from ‘package:dplyr’:

    select

The following object is masked from ‘package:RobStatTM’:

    oats

columnas=c(1:485,495:590,591:599,605:615,630:649)
mfeat.train<-ds.train.x[columnas]#cbind(fou,pix,zer,kar)#cbind(fou,fac,kar,pix,zer,mor)
colnames(mfeat.train)<-as.vector(seq(1,length(mfeat.train),1))

mfeat.test = ds.test.x[columnas]
colnames(mfeat.test)<-as.vector(seq(1,length(mfeat.test),1))

set.seed(100)
modelo_lda <- lda(formula = ds.train$class ~ . ,data = mfeat.train)

predicciones.train <- predict(object = modelo_lda, newdata = mfeat.train)

Error in UseMethod("predict") : 
  no applicable method for 'predict' applied to an object of class "list"

predicciones.test <- predict(object = modelo_lda, newdata = mfeat.test)
table(ds.test$class, predicciones.test$class, dnn = c("Clase real", "Clase predicha"))

          Clase predicha
Clase real  0  1  2  3  4  5  6  7  8  9
         0 71  0  0  0  0  0  0  0  0  0
         1  0 49  0  1  1  0  0  1  0  1
         2  0  0 56  0  0  0  0  0  0  0
         3  0  1  1 62  0  0  0  0  0  0
         4  0  0  0  0 54  0  0  0  0  0
         5  0  0  0  0  0 57  0  0  0  0
         6  0  0  0  0  0  1 51  0  0  0
         7  0  0  1  0  0  0  0 65  0  0
         8  0  0  0  0  0  0  0  0 68  0
         9  0  1  0  1  0  0  0  0  0 57

test_error <- mean(ds.test$class != predicciones.test$class) * 100
paste("test_error =", test_error, "%")

[1] "test_error = 1.66666666666667 %"

QDA

#columnas=c(485:495,630:649,1:80,110:120,140:145,450:480)#c(1:485,495:590,591:599,605:615,630:649)
columnas=c(485:495,630:649,1:80)
mfeat.train<-ds.train.x[columnas]#cbind(fou,pix,zer,kar)#cbind(fou,fac,kar,pix,zer,mor)
colnames(mfeat.train)<-as.vector(seq(1,length(mfeat.train),1))

mfeat.test = ds.test.x[columnas]
colnames(mfeat.test)<-as.vector(seq(1,length(mfeat.test),1))

set.seed(100)
#target = ds.train$class
#ds.qda.train = mfeat.train

target = rbind(ds.train,ds.train,ds.train,ds.train,ds.train,ds.train,ds.train,ds.train)$class
ds.qda.train =rbind(mfeat.train,mfeat.train,mfeat.train,mfeat.train,mfeat.train,mfeat.train,mfeat.train,mfeat.train)

modelo_qda <- qda(formula = target ~ ., data=ds.qda.train)

qda.predicciones.train <- predict(object = modelo_qda, newdata = mfeat.train)
table(ds.train$class, qda.predicciones.train$class, dnn = c("Clase real", "Clase predicha"))

          Clase predicha
Clase real   0   1   2   3   4   5   6   7   8   9
         0 129   0   0   0   0   0   0   0   0   0
         1   0 147   0   0   0   0   0   0   0   0
         2   0   0 144   0   0   0   0   0   0   0
         3   0   0   0 136   0   0   0   0   0   0
         4   0   0   0   0 146   0   0   0   0   0
         5   0   0   0   0   0 143   0   0   0   0
         6   0   0   0   0   0   0 148   0   0   0
         7   0   0   0   0   0   0   0 134   0   0
         8   0   0   0   0   0   0   0   0 132   0
         9   0   0   0   0   0   0   0   0   0 141

trainig_error <- mean(ds.train$class != qda.predicciones.train$class) * 100
paste("trainig_error =", trainig_error, "%")

[1] "trainig_error = 0 %"

qda.predicciones.test <- predict(object = modelo_qda, newdata = mfeat.test)
table(ds.test$class, qda.predicciones.test$class, dnn = c("Clase real", "Clase predicha"))

          Clase predicha
Clase real  0  1  2  3  4  5  6  7  8  9
         0 64  2  0  0  4  1  0  0  0  0
         1  0 52  0  1  0  0  0  0  0  0
         2  0  3 52  0  0  0  0  0  0  1
         3  0  2  0 56  0  6  0  0  0  0
         4  0  2  0  1 50  0  1  0  0  0
         5  0  3  0  0  0 54  0  0  0  0
         6  0  2  0  0  0  0 50  0  0  0
         7  0  4  1  0  0  0  0 59  0  2
         8  0  6  0  2  0  2  0  0 58  0
         9  0  3  0  0  0  1  0  0  0 55

test_error <- mean(ds.test$class != qda.predicciones.test$class) * 100
paste("test_error =", test_error, "%")

[1] "test_error = 8.33333333333333 %"

PCA + QDA

          Clase predicha
Clase real   0   1   2   3   4   5   6   7   8   9
         0 129   0   0   0   0   0   0   0   0   0
         1   0 147   0   0   0   0   0   0   0   0
         2   0   0 144   0   0   0   0   0   0   0
         3   0   0   0 136   0   0   0   0   0   0
         4   0   0   0   0 146   0   0   0   0   0
         5   0   0   0   0   0 143   0   0   0   0
         6   0   0   0   0   0   0 148   0   0   0
         7   0   0   0   0   0   0   0 134   0   0
         8   0   0   0   0   0   0   0   0 132   0
         9   0   0   0   0   0   0   0   0   0 141
[1] "trainig_error = 0 %"
          Clase predicha
Clase real  0  1  2  3  4  5  6  7  8  9
         0 69  0  0  0  0  1  0  0  1  0
         1  0 51  0  0  0  2  0  0  0  0
         2  0  0 54  0  0  0  0  0  0  2
         3  0  0  1 63  0  0  0  0  0  0
         4  0  1  0  0 52  0  1  0  0  0
         5  0  0  0  0  0 57  0  0  0  0
         6  0  0  0  0  0  1 51  0  0  0
         7  0  0  0  0  0  0  0 63  0  3
         8  0  0  0  0  0  2  0  0 66  0
         9  0  1  0  0  0  0  0  0  0 58
[1] "test_error = 2.66666666666667 %"

PCA+LDA

library(factoextra)
#Hago el PCA
res.pca <- prcomp(as.matrix(scale(ds.train.x)), scale = T, center=T, rank. = 70)

mfeat.train = as.data.frame(res.pca$x)
colnames(mfeat.train)<-as.vector(seq(1,length(mfeat.train),1))

mean_ds.train.x = apply(X = ds.train.x, MARGIN = 2, FUN = mean)
var_ds.train.x = apply(X = ds.train.x, MARGIN = 2, FUN = var)

mfeat.test =  as.data.frame(as.matrix(scale(ds.test.x)) %*% res.pca$rotation) 
colnames(mfeat.test)<-as.vector(seq(1,length(mfeat.test),1))

set.seed(100)
target = ds.train$class
ds.lda.train = mfeat.train

modelo_lda <- lda(formula = target ~ ., data=ds.lda.train)

lda.predicciones.train <- predict(object = modelo_lda, newdata = mfeat.train)
table(ds.train$class, lda.predicciones.train$class, dnn = c("Clase real", "Clase predicha"))

          Clase predicha
Clase real   0   1   2   3   4   5   6   7   8   9
         0 128   0   0   0   0   0   0   0   1   0
         1   0 145   0   0   1   0   0   0   0   1
         2   0   0 144   0   0   0   0   0   0   0
         3   0   2   0 132   1   1   0   0   0   0
         4   0   0   0   0 145   0   0   0   0   1
         5   0   1   0   2   0 138   0   0   0   2
         6   0   1   0   0   1   0 146   0   0   0
         7   0   0   0   0   0   0   0 133   0   1
         8   0   0   0   0   0   0   0   0 131   1
         9   0   1   0   0   0   0   0   0   0 140

trainig_error <- mean(ds.train$class != lda.predicciones.train$class) * 100
paste("trainig_error =", trainig_error, "%")

[1] "trainig_error = 1.28571428571429 %"

lda.predicciones.test <- predict(object = modelo_lda, newdata = mfeat.test)
table(ds.test$class, lda.predicciones.test$class, dnn = c("Clase real", "Clase predicha"))

          Clase predicha
Clase real  0  1  2  3  4  5  6  7  8  9
         0 70  0  0  0  0  0  0  0  1  0
         1  0 51  0  0  1  0  1  0  0  0
         2  0  0 56  0  0  0  0  0  0  0
         3  0  1  1 62  0  0  0  0  0  0
         4  0  0  0  0 53  1  0  0  0  0
         5  0  1  0  0  0 56  0  0  0  0
         6  0  0  0  0  0  0 52  0  0  0
         7  0  0  1  0  0  0  0 65  0  0
         8  0  0  0  0  0  0  1  0 67  0
         9  0  1  0  0  0  0  0  0  0 58

test_error <- mean(ds.test$class != lda.predicciones.test$class) * 100
paste("test_error =", test_error, "%")

[1] "test_error = 1.66666666666667 %"

summary(res.pca)

Importance of first k=70 (out of 649) components:
                          PC1     PC2     PC3     PC4     PC5     PC6     PC7     PC8     PC9    PC10
Standard deviation     9.7405 8.01229 7.51485 6.11207 5.66913 5.07823 4.59006 4.15344 3.89448 3.82865
Proportion of Variance 0.1462 0.09892 0.08702 0.05756 0.04952 0.03974 0.03246 0.02658 0.02337 0.02259
Cumulative Proportion  0.1462 0.24511 0.33212 0.38968 0.43920 0.47894 0.51140 0.53798 0.56135 0.58394
                          PC11    PC12    PC13    PC14    PC15    PC16    PC17    PC18    PC19    PC20
Standard deviation     3.33982 3.20288 3.01899 2.85840 2.78533 2.74263 2.55386 2.48785 2.35503 2.26616
Proportion of Variance 0.01719 0.01581 0.01404 0.01259 0.01195 0.01159 0.01005 0.00954 0.00855 0.00791
Cumulative Proportion  0.60113 0.61693 0.63098 0.64357 0.65552 0.66711 0.67716 0.68670 0.69524 0.70315
                          PC21    PC22    PC23    PC24    PC25    PC26    PC27    PC28    PC29    PC30
Standard deviation     2.17500 2.10937 2.07704 2.01044 1.93244 1.92075 1.86297 1.82420 1.81026 1.77779
Proportion of Variance 0.00729 0.00686 0.00665 0.00623 0.00575 0.00568 0.00535 0.00513 0.00505 0.00487
Cumulative Proportion  0.71044 0.71730 0.72395 0.73017 0.73593 0.74161 0.74696 0.75209 0.75714 0.76201
                          PC31    PC32    PC33    PC34    PC35    PC36   PC37    PC38    PC39    PC40
Standard deviation     1.75107 1.70085 1.65768 1.62921 1.58459 1.55223 1.5490 1.48758 1.47890 1.46167
Proportion of Variance 0.00472 0.00446 0.00423 0.00409 0.00387 0.00371 0.0037 0.00341 0.00337 0.00329
Cumulative Proportion  0.76673 0.77119 0.77542 0.77951 0.78338 0.78709 0.7908 0.79420 0.79757 0.80086
                          PC41    PC42    PC43    PC44    PC45    PC46    PC47    PC48   PC49    PC50
Standard deviation     1.44632 1.42805 1.38908 1.37539 1.36577 1.35458 1.32035 1.30902 1.2991 1.29030
Proportion of Variance 0.00322 0.00314 0.00297 0.00291 0.00287 0.00283 0.00269 0.00264 0.0026 0.00257
Cumulative Proportion  0.80409 0.80723 0.81020 0.81312 0.81599 0.81882 0.82150 0.82414 0.8267 0.82931
                          PC51    PC52    PC53    PC54    PC55    PC56    PC57    PC58    PC59    PC60
Standard deviation     1.28652 1.27702 1.26287 1.25259 1.23779 1.23076 1.20471 1.19300 1.17894 1.17229
Proportion of Variance 0.00255 0.00251 0.00246 0.00242 0.00236 0.00233 0.00224 0.00219 0.00214 0.00212
Cumulative Proportion  0.83186 0.83437 0.83683 0.83925 0.84161 0.84394 0.84618 0.84837 0.85051 0.85263
                          PC61    PC62    PC63    PC64    PC65    PC66    PC67    PC68   PC69    PC70
Standard deviation     1.15686 1.15100 1.12883 1.12483 1.11538 1.09626 1.09252 1.08332 1.0802 1.06924
Proportion of Variance 0.00206 0.00204 0.00196 0.00195 0.00192 0.00185 0.00184 0.00181 0.0018 0.00176
Cumulative Proportion  0.85469 0.85673 0.85870 0.86065 0.86256 0.86442 0.86626 0.86806 0.8699 0.87162

Graficar algo?

library(klaR)

png(filename = "LDA_regiones_cp123.png", width = 800, height = 600)
partimat(formula = target ~ ds.lda.train$`1` + ds.lda.train$`2` + ds.lda.train$`3`,  plot.matrix = TRUE, imageplot = TRUE,
         data=ds.lda.train, 
         method = "lda", 
         prec = 200,
         nplots.vert = 1 ,
         nplots.hor = 1,
         col.mean = "green",
         name=c("PC1","PC2","PC3"))
dev.off()

null device 
          1 

partimat(formula = target ~ ds.lda.train$`1` + ds.lda.train$`2` + ds.lda.train$`3`+ ds.lda.train$`4`, 
         data=ds.lda.train, 
         method = "lda", 
         prec = 200,
         nplots.vert = 1 ,
         nplots.hor = 1,
         name=c("PC1","PC2"))

partimat(formula = target ~ ds.qda.train$`1` + ds.qda.train$`2`, plot.matrix = TRUE, imageplot = FALSE,
         data=ds.qda.train, 
         method = "qda", 
         prec = 200,
         nplots.vert = 1 ,
         nplots.hor = 1,
         col.mean = "green",
         name=c("PC1","PC2")
         )

png(filename = "QDA_regiones_cp123.png", width = 800, height = 600)
partimat(formula = target ~ ds.qda.train$`1` + ds.qda.train$`2` + ds.qda.train$`3`, 
         data=ds.qda.train,  plot.matrix = TRUE, imageplot = TRUE,
         method = "qda", 
         prec = 200,
         nplots.vert = 1 ,
         nplots.hor = 1,
         col.mean = "green",
         name=c("PC1","PC2","PC3")
         )
dev.off()

null device 
          1 

boxM(data = ds.lda.train, grouping = ds.train$class)

    Box's M-test for Homogeneity of Covariance Matrices

data:  ds.lda.train
Chi-Sq (approx.) = 83331, df = 22365, p-value < 2.2e-16

royston_test <- mvn(data = ds.lda.train, mvnTest = "royston", multivariatePlot = "qq")

royston_test$multivariateNormality

---

METRICAS MULTI-K

metricasMulti = function(class_orig,class_pred,vector_class){
  kk=c()
  
  for(k in vector_class){
    
    aux = ifelse(class_orig==k,1,0)
    aux_pred = ifelse(class_pred==k,1,0)
    Nk = sum(aux)
    
    TPk = sum(ifelse(aux==1 & aux_pred==1,1,0)) 
    TNk = sum(ifelse(aux==0 & aux_pred==0,1,0))
    FPk = sum(ifelse(aux==0 & aux_pred==1,1,0))
    FNk = sum(ifelse(aux==1 & aux_pred==0,1,0))

    accuracy_k =  (TPk + TNk) / (TPk+TNk+FPk+FNk)
    precision_k =  TPk / (TPk+FPk)
    recall_k = TPk / (TPk+FNk)
    F1_k = TPk / (TPk + 0.5*(FPk+FNk))
    
    kk <- rbind(kk,c(k,round(accuracy_k,3),round(precision_k,3),round(recall_k,3),round(F1_k,3),TPk,TNk,FPk,FNk,Nk))
  }
  
  
  ds.metrics = data.frame(kk)
  names(ds.metrics) <- c("class","accuracy","precision","recall","F1","TP","TN","FP","FN","Nk")
  ds.metrics = rbind(ds.metrics, apply(ds.metrics, FUN="mean", MARGIN = 2))
  ds.metrics[11,1] = "mean"
  return(ds.metrics)
  }

vector_class = c(0,1,2,3,4,5,6,7,8,9)
metrics_multi = metricasMulti(ds.test$class,lda.predicciones.test$class,vector_class = vector_class)

metrics_multi

---

ds.train.pca =  as.data.frame(as.matrix(ds.train[,1:640])%*%res.pca$rotation)
ds.test.pca =  as.data.frame(as.matrix(ds.test[,1:640])%*%res.pca$rotation)


pred_train = predict(model_tree_pca, ds.train.pca, type="class")
pred_test = predict(model_tree_pca, ds.test.pca, type="class")
#error de clasificación 
mean(ifelse(ds.train.n$class==pred_train,1,0)) 
mean(ifelse(ds.test.n$class==pred_test,1,0)) 

apply(X = ds.train[,1:10], MARGIN = 2, FUN = mean)

library(FactoMineR)

res.pca2 <- PCA(X = ds.train.x[,1:10], scale.unit = FALSE, ncp = 4, graph = TRUE)

((as.matrix(ds.train.x[,1:10])-res.pca2$call$centre) %*% (res.pca2$var$coord))[1:10,]

res.pca2$ind$cos2[1,]

---

library(glmnet)

set.seed(110)

XX<-model.matrix(lm(class~.,data=ds.train))
Xtest<-model.matrix(lm(class~.,data=ds.test))

cv.lasso<-cv.glmnet(x=XX,y=ds.train$class,family="multinomial",alpha=1,nfolds=3,trace.it=1)
ajustelasso<-glmnet(x=XX,y=ds.train$class,family="multinomial",alpha=1,lambda=cv.lasso$lambda.1se, trace.it=1)
mean(predict(ajustelasso,newx=Xtest,type="class")==ds.test$class)

library(caret)

car::vif(lm(fac[,3]~.,data=fac[1:55]))

heatmap(cor(fac),  Rowv = NA, Colv = NA)

heatmap(cor(subset(ds.train, select=c(-class))),  Rowv = NA, Colv = NA)